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I have calculated p-values of two independent groups (each group contains 17 samples and each sample is 100 points). I used scipy's mann whitney u test. Further, I combined the p-values using Fisher's method as suggested by one of my colleagues. However, the p-values are just too small to make any sense to me. Here is a sample output:

import scipy.stats as stats
p_value_list = [3.3629559156133476e-56, 1.966307600030748e-254, 6.3484089727582271e-103, 
                3.1221165197874102e-92, 5.8797795864262639e-128, 4.0807369798923832e-130, 
                1.205918004734663e-187, 8.9953478731039129e-19, 2.1492251770664035e-127, 
                0.11623743456915718, 6.182421882338173e-13, 3.7920992534448722e-112, 3.5888837913096105e-97, 
                7.5565994692959197e-134, 0.0026669650138866794, 4.0844220972198632e-16, 4.583685848455044e-95]
results= stats.combine_pvalues(p_value_list)
print (results)

Which gives the following output (p is zero!)

(7172.864625387464, 0.0)

Now, my questions are:

  • What is the meaning of small p-values (something like 1.2e-187)?
  • How to interpret a p-value that is zero?
  • Since I am writing a paper based on this calculation, how can one report this in a peer-reviewed journal?
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  • $\begingroup$ With P-values that small you should be able to discern the difference as bloody obvious even without any statistical procedure. Is that a fair description of your results? If not, then you have done something wrong in the calculation. $\endgroup$
    – Michael Lew
    Feb 12, 2017 at 7:20
  • $\begingroup$ Your combined P-value is calculated assuming the 17 P-values are all tests of the same null hypothesis. Is that really the case? You need to give a lot more detail about your data before a clear answer to your questions is possible. $\endgroup$
    – Michael Lew
    Feb 12, 2017 at 7:25
  • $\begingroup$ See this: stats.stackexchange.com/questions/78839 $\endgroup$
    – amoeba
    Feb 12, 2017 at 7:37

1 Answer 1

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  1. A P-value of $10^{-187}$ is very strong evidence that the null hypothesis is not true, or that the statistical model used is inappropriate. Very strong indeed.

  2. A P-value of zero occurs when the report runs out of decimal places. A P-value of $10^{-187}$ is not really different from a P-value of zero for most purposes.

  3. Present the data and a measure of the effect size in addition to the P-values.

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